Class 11MathematicsTrigonometrical Ratios, Functions and IdentitiesMix Examples-Trigonometrical Ratios, Functions and Identities
EasyIf $\sin A + \cos A = \sqrt{2}$,then $\cos^2 A = $
- A$\frac{1}{4}$
- B$\frac{1}{2}$
- C$\frac{1}{\sqrt{2}}$
- D$\frac{3}{2}$
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If $\tan A$ and $\tan B$ are the roots of the quadratic equation $x^2-px+q=0$,then $\sin^2(A+B)$ is equal to
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View SolutionIf $\alpha$ is a root of $25\cos^2\theta + 5\cos\theta - 12 = 0$ and $\pi/2 < \alpha < \pi$,then $\sin 2\alpha$ is equal to:
Medium
View SolutionIf $0 \leq A, B \leq \frac{\pi}{4}$ and $\cot A + \cot B + \tan A + \tan B = \cot A \cot B - \tan A \tan B$,then $\sin(A + B) = $
If $15 \sin^{4} \alpha + 10 \cos^{4} \alpha = 6$ for some $\alpha \in R$,then the value of $27 \sec^{6} \alpha + 8 \operatorname{cosec}^{6} \alpha$ is equal to ....... .
$3\left[ \sin^4\left( \frac{3\pi}{2} - \alpha \right) + \sin^4(3\pi + \alpha) \right] - 2\left[ \sin^6\left( \frac{\pi}{2} + \alpha \right) + \sin^6(5\pi - \alpha) \right] = $
DifficultIIT 1986
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